Occham's Razor

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Efficient reasoning
One important contribution that he made to modern science and modern intellectual culture was efficient reasoning with the principle of parsimony in explanation and theory building that came to be known as Occam's Razor. This maxim, as interpreted by Bertrand Russell,[15] states that if one can explain a phenomenon without assuming this or that hypothetical entity, there is no ground for assuming it, i.e. that one should always opt for an explanation in terms of the fewest possible causes, factors, or variables. He turned this into a concern for ontological parsimony; the principle says that one should not multiply entities beyond necessity – Entia non sunt multiplicanda sine necessitate – although this well-known formulation of the principle is not to be found in any of Ockham's extant writings.[16] He formulates it as: "For nothing ought to be posited without a reason given, unless it is self-evident (literally, known through itself) or known by experience or proved by the authority of Sacred Scripture."[17] For Ockham, the only truly necessary entity is God; everything else is contingent. He thus does not accept the principle of sufficient reason, rejects the distinction between essence and existence, and advocates against the Thomistic doctrine of active and passive intellect. His scepticism to which his ontological parsimony request leads appears in his doctrine that human reason can prove neither the immortality of the soul nor the existence, unity, and infinity of God. These truths, he teaches, are known to us by revelation alone.

Natural philosophy
Ockham wrote a great deal on natural philosophy, including a long commentary on Aristotle's Physics. According to the principle of ontological parsimony, he holds that we do not need to allow entities in all ten of Aristotle's categories; we thus do not need the category of quantity, as the mathematical entities are not "real". Mathematics must be applied to other categories, such as the categories of substance or qualities, thus anticipating modern scientific renaissance while violating Aristotelian prohibition of metabasis.
Theory of knowledge
In the theory of knowledge, Ockham rejected the scholastic theory of species, as unnecessary and not supported by experience, in favour of a theory of abstraction. This was an important development in late medieval epistemology. He also distinguished between intuitive and abstract cognition; intuitive cognition depends on the existence or non existence of the object, whereas abstractive cognition "abstracts" the object from the existence predicate. Interpreters are, as yet, undecided about the roles of these two types of cognitive activities.